Whisk flour, salt, and sugar in a large bowl. Cut in cold butter until mixture resembles coarse crumbs. Add ice water 1 tablespoon at a time, mixing until dough holds together. Form into a disk, wrap in plastic, and refrigerate for at least 30 minutes.
Preheat oven to 375°F. On a floured surface, roll dough into a 12-inch circle. Transfer to a 9-inch pie dish, trim excess, and crimp edges. Prick bottom with a fork, line with parchment, and fill with pie weights. Blind bake for 15 minutes, remove weights, and bake 5 more minutes until set and pale. Reduce oven temperature to 325°F.
In a clean, dry bowl, whip egg whites with lemon juice using an electric mixer until soft, glossy peaks form, about 2-3 minutes. Set aside.
In a saucepan over medium heat, warm evaporated milk and sweetened condensed milk until small bubbles form around the edge (do not boil). In another bowl, whisk egg yolks with sugar and salt until pale and thickened. Slowly whisk a little warm milk into the yolk mixture to temper, then gradually add the rest. Stir in vanilla. Strain the mixture through a fine mesh sieve into a clean bowl.
Whisk about one-third of the whipped egg whites into the custard base to loosen. Gently fold in the remaining egg whites with a rubber spatula until no white streaks remain, being careful not to deflate the mixture.
Pour the custard filling into the blind-baked crust, filling almost to the top. Bake on the middle rack at 325°F for 35-45 minutes until the top is deep golden brown and the center jiggles slightly but is not liquid. Cover edges with foil if browning too quickly. Cool completely on a wire rack.
Once the pie has cooled to room temperature, refrigerate for at least 2 hours to fully set. Slice with a sharp knife, wiping the blade between cuts for neat pieces.